The long-term objective of this research is the development of statistical tools to improve scientific inference in cancer research, with a principal focus on the elucidation of the long-term effects of prevention and treatment interventions for breast cancer. A primary objective is to provide flexible semiparametric models to estimate and predict the population impact of prevention and adjuvant therapy on breast cancer using data from cancer screening trials and large prevalent cohort studies. Research will include a focus on methods that adjust for different biases encountered in such studies. A continuing effort is to provide a quantitative framework to determine optimal cancer screening schedules by balancing benefit and cost. The specific aims of this competing renewal include: (1) to develop and evaluate a class of semiparametric density ratio models to test a treatment effect in right-censored length-biased data; (2) to develop a unified estimation and prediction tool for semiparametric transformation models applied to right- censored length-biased data; (3) to develop robust and efficient estimation and prediction procedures for semiparametric accelerated failure time models on right-censored length-biased data; (4) to develop estimation and prediction methods for data of uncertain time of disease initiation with or without a cure probability; (5) to optimize screening programs using decision theoretic approaches by explicitly incorporating different risk profiles and natural history distributions into the general model structure; and (6) to develop user-friendly computer codes linked to existing software for the medical and statistical communities.